generateCauchyScaled(x0, gamma, desiredMin, desiredMax, LQpercent, UQpercent, lowerQuantile, upperQuantile)
Overview
The function generates a scaled random number based on a Cauchy distribution with a specified location parameter ( x_0 ) and scale parameter ( \gamma ) within the desired range.
Parameters
| Parameter | Type | Description |
|---|---|---|
x0 |
Number | The location parameter of the Cauchy distribution. |
gamma |
Number | The scale parameter of the Cauchy distribution. |
desiredMin |
Number | The minimum desired value of the scaled random number. |
desiredMax |
Number | The maximum desired value of the scaled random number. |
LQpercent |
Number | Lower quantile percentage. Default is 0.001. |
UQpercent |
Number | Upper quantile percentage. Default is 0.999. |
lowerQuantile |
Number | Lower quantile value. Calculated by default if not provided. |
upperQuantile |
Number | Upper quantile value. Calculated by default if not provided. |
Returns
| Return | Type | Description |
|---|---|---|
random |
Number | A scaled random number in the range [desiredMin, desiredMax]. |
Example
local random = StatBook.generateCauchyScaled(0, 1, -10, 10)
print(random) -- Output will vary
Mathematical Background
The function generates a random number x that follows a Cauchy distribution and then scales it to the desired range. The formula used for scaling is:
\text{random} = \text{scaleToDesiredRange}(x, \text{lowerQuantile}, \text{upperQuantile}, \text{desiredMin}, \text{desiredMax})
Where scaleToDesiredRange is a function that takes the random number x , lower and upper quantile values, and desired minimum and maximum values as arguments, and returns a scaled value that falls within [desiredMin, desiredMax].